Question 54200: Can anyone help me with this word problem:
Hanson drove his rig at x mph for 3 hours, then increased his speed to x + 15 and drove for 2 more hours. Write a polynomial that represents the total distance that he traveled. Find the distance if x=45 mph.
Thanks in advance for any help you can provide.
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! Using the formula for distance, d = rt. Where d = distance, r = rate (speed), and t = the time taken for the trip.
The distance (d1) for the first leg can be written:
d1 = (x mph)(3 hrs)
d1 = 3x
For the second leg, the distance (d2) can be written:
d2 = (x+15)mph(2 hrs)
d2 = 2x+30
The total distance, D, is d1+d2 or 3x + 2x+30, simplifying this you get:
D = 5x+30 as the polynomial that represents the total distance traveled.
If the speed, x = 45 mph, the the total distance is:
D = 5(45) + 30
D = 225 + 30
D = 255 miles.
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